LA HW and Cale

Linear Algebra Schedule, Spring 2012

I've grouped the class meetings into seven blocks, of two weeks each. You will have a quiz on the second Thursday of the block, mostly related to the homework [HW] and lectures and reading for the previous 2-3 weeks, but not from the week of the Quiz. For example, Quiz 2 will be in Week 4 and will mainly cover topics from Weeks 2 and 3. There may be a little overlap of topics, between Quiz 1 and Quiz 2, for example. The HW lists below are intended to be the minimal required to get by. You should do at least 50 per cent more. I will probably have to adjust some dates and content from time to time, but will announce changes on this web page asap, and announce any major changes also in class.

In previous terms, HW was collected and graded. I refered to the HW for Quiz 1 as HW1, etc, and may continue with that abbreviation, though it means less in Spring 2012 than it once did.

How to read the tables: As you can see from the tables below, I expect to cover about 1 section of our book per lecture. Quiz 1 is 1/19 and mainly covers ideas in HW1 (eg, Ch 1.1 and 1.2). Don't worry too much about the abbreviations under "lecture topics" as those are mainly notes for myself. Contact me ASAP if you don't understand anything, or you see a conflict with a religious holiday, or any other mistake. I usually give a little extra credit for such help.

These first weeks should be the easiest, unless you are very rusty at math. You will be learning to solve systems, and may have to adjust to a math course which emphasizes vocabulary [and later on, theorems] much more than Calculus does. You should also be learning to use MATLAB. See my MATLAB page for tips and for the separate MHW lists.

Read Ch 1 [but I won't test you on Ch 1.6, Partitioned Matrices]. Learn the main concepts, which are usually highlighted (such as consistent system, equivalent systems, augmented matrix, triangular form, elem operations, row echelon form, G.elim'n, underdetermined, etc). Do HW 1, and more problems as needed. Read over the other exercises, including Ch 1.1 - 9 and Ch. 1.2 - 13 to 19. Start on HW2. Look over Leon's website and this one, and practice with my page, proofwriting Part I, if needed.

In case I'm scaring you, remember that Quiz 1 will be mostly like HW 1. In previous terms, the Quiz 1 average has usually been high, over 70 percent. You can find sample quizzes (and keys) on my exam page. If you are having any problems, feel free to visit me or Eric, or email me with questions. On the other hand, if you have any extra time after mastering Ch 1, I strongly suggest that you scan Chapters 2-6 (especially Chapter 3), to let those ideas soak in for a while.

We have a Learning Assistant for the two sections of MAS 3105 this Spring, Eric W, also president of the FIU Math Club. He will be in DM409A, the MathStat computer lab, for you

Tuesday Thursday 12:45pm-1:45pm
Tuesday 3:30-4:30pm
Thursday 5:00-6:00pm
Friday 4:00-5:00pm

Some PCs in DM 409A also have MATLAB. If that room is taken, look for Eric at the large table just outside that room. This should be the first place you go for help ! Some other tutoring options are listed on my "help pages". If you find any info there which is out of date, pls tell me. The following [still valid?] message is from the Math Dept in 2009, "Tutoring services are available this semester in a much better location: Green Library - GL 129 and suite! The schedule is Mondays-Thursdays 9am-8pm, Fridays 9am-5pm." (this note is not specifically about MAS 3105). You are also welcome in DM419B during my office hours.

There have been several questions in the past about HW problem, Ch 1.3 - 9, [recently corrected - in the 7th Ed, it was 1.3-13] so here is a similar example. If several people this term ask about such a problem, I may post a new page for that. Some HW1 exercises may seem a bit tedious to do by hand. You can use MATLAB to save some time on such problems, but you will not have MATLAB during the Quizzes, just a pencil !

Day	Date	I give you	You give me	Lecture topics	HW
1	T 1/10	Web site		1.1- Systems, G.Elim	1ab, 2, 3, 4, 6ab, 7
2	R 1/12			1.2- RE form, HW1	1, 2abc, 3abc, 4, 5achi,12, 13, 14, 15
3	T 1/17			1.3- Matrix Arith 1.4- Matrix Algebra	1.3 - 1, 2, 3, 4, 6, 9, 10 1.4 - 1, 3, 4, 7, 10, 16, 29
4	R 1/19	Quiz 1 thru 1.2		1.5- Elem.Mat's	1.5 - 1, 2, 3, 5, 6, 10abef, 12, 18, 24 1.6 - 1 [just scan this section quickly]

For Quiz 2, read Chs 1.3 - 2.2 and review your lecture notes thru 1/26. Focus on the main definitions and theorems. Prepare to prove the "tfae" Thm 1.5.2, and Thms 2.2.2 and 2.2.3 . Review HW2, and do more problems as needed, such as 1.4-16. Practice with the Chapter Tests, such as on page 81. Always try to justify your True-False answers, at least for yourself (it is sometimes required on my quizzes, but usually not). You can practice with my old quizzes on the exam page, but don't expect to see the same questions on your quiz.

You should be working on the Matlab HW from Chapter 1 by now, and starting to complain about closed labs, dead printers, arcane exercises, etc. Do it early! Starting with Quiz 2, I may ask some very easy questions about MATLAB. As long as you are keeping up with the schedule, you shouldn't really have to study for these.

NOTE from Feb 1 - I was really hoping to post more about Q2, but my main computer died, putting me behind schedule. The notes above will have to do. But if you need more help with the proof of Thm 2.2.3, you can look here. (this does NOT imply that Thm 2.2.3 will be on Q2 !!) I will try to keep Q2 very straightforward, and will wait to test you on induction proofs.

HW2 grading and your proofs - [Written based on HW2 papers from 2009 or so, but probably just as relevant to 2012 students] - "If you aren't getting your proofs right yet, this is something you should work on asap, perhaps with me or with Eric. Remember to include WORDS but (usually) not examples. The average was about 75 / 100. If you feel lost on proof-writing, try my help page drills thru Part III or come by my office hours for help. There are also a few good books on proofs (eg Velleman's) you can buy at a local bookstore if you need to spend more time on this."

Problem 2.2.20 sometimes causes trouble (but is interesting - see also 2.2.21). I think there is a help page for this problem. Problem 3.1.7 is easy if you can set it up correctly - you might assume that the space has 2 "zeros", called a and b, for example.

A student found this link to the errata list for our book, from the author's site. Thanks!

Day	Date	I give you	You give me	Lecture topics	HW
5	T 1/24			2.1 - Det(A)	1, 2, 3abcg, 4, 8, 10
6	R 1/26			2.2 - Det's + E's	1, 5, 6, 7, 13, 15, 20
7	T 1/31			some pfs and 2.3	1, 2abc, 3, 12, 14
8	R 2/2	Quiz 2 thru 2.2		3.1- vec-sp's/HW	1, 3 (has 8 parts), 7

The course enters more abstract territory this week, so pay more attention to vocabulary and precise definitions. Note that MHW1 is due Tuesday. The program is on many machines in PC 413 and on 2 slow ones in DM 409A [near the door]. See the MATLAB page. If interested, see this old HW3 grading page, from 2010.

Quiz 3 may include an induction pf from Ch 2 (see page 90 and the Ch 2.2 exercises). It will cover mainly HW3 [eg weeks 6 and 7], and Chs 2.1 thru 3.2, maybe easy parts of 3.3. Know the proofs of Thms 2.3.1 and Thms 3.2.1. You can also practice the 2 TF quizzes on my exam page and the Ch 2 and Ch. 3 help pages. My quizzes may overlap a little [for example, Ch 2.2 could be on both Quiz 2 and Quiz 3]. Remember - try to do more than the assigned HW!

Day	Date	I give you	You give me	Lecture topics	HW
9	T 2/7		MHW1	3.2 subsp's, span, N(A)	1, 3, 4, 12, 18, 20
10	R 2/9			3.3 LD, Col(A), basis	1, 2, 3, 8, 14, 15, 19
11	T 2/14			3.4- basis, w pfs	1, 2, 3, 5, 7, 11, 14
12	R 2/16	Quiz 3 thru 3.3		more 3.4, and HW prep

This rest of this page is under construction - do not trust it yet. You may use it to get some idea of what we will cover this term.

The most of the rest of this page is left over from 2011, and will be updated asap. Mainly, I haven't checked all the changes in the 8th Edn.

We went over the "Rabbit Example" on Tues Feb 22 - make sure you understand that, as I will refer back to that repeatedly.

Grading HW 4 = 30 points each for 3.4.11 and 3.5.6a, + 40 points completeness / general. The average score on HW is running pretty high now. The most common problem is not showing enough work. I didn't grade any proofs this time - see me if you are uncertain about any of those answers.

Quiz 4 covers HW 4 and the reading thru 3.6. If you are having trouble with proofs, see my hints for HW4. Know the main definitions, and the proofs of Thms 3.3.2, 3.4.3 and 3.6.1. Be able to use the Wronskian for problems like HW 3.3.6 and 7. You can also prepare by trying the three Ch 3 TF quizzes on my exam page.

Day	Date	I give you	You give me	Lecture topics	HW
13	T 2/21			3.5+, transition m's	1, 2, 5, 6, 9
14	R 2/23			3.6-, col(A), Ker	1, 4, 5, 9, 19
15	T 2/28			4.1, HW, appl'n	1, 2, 3, 4, 7, 14, 20, 21
16	R 3/1	Quiz 4 thru 3.6		4.2+, mat.reps, P_4	1, 2, 5, 6, 14, 18

Quiz 5 covers HW 5 and the reading thru 5.1. Understand what each theorem says. Know the proofs of Thms 3.6.5, 3.6.6, 4.1.1 and 5.1.1. There are 2 TF quizzes for you on the exam page. The HW in Ch 4.3 has some good proofs ( try 4.3 - 12, 13 and 14). Review the "Rabbit Ex" from the lectures; a quiz problem might refer to it. Also, review MHW2 before you hand it in.

I have posted some hints for the Ch 5.2 HW. Also, some sample proofs related to Chs 4.1 thru 5.1.

March 28 is the deadline for changing the class roster (I will post it here approx March 18). Make sure you are listed there (with the "Graded" label) if you want a grade, and that you are not listed, or listed as "Admin", if you dropped.

Day	Date	I give you	You give me	Lecture topics	HW
18	T 3/6			4.3+ sim'y, scalar prod	1, 2, 5, 7, 9, 11
19	R 3/8			5.1+ planes, perps	1, 2, 4, 5, 8, 9
20	Break T 3/20		MHW2	5.2 R(A^T), sums, HW	1, 2, 3, 5, 13
21	R 3/22	Quiz 5 thru 5.1		5.3 - L Sq's	1, 2, 3, 5

Note on reading Ch 5: We will move fairly quickly through Ch 5.3 to 5.6, because many parts are optional at FIU. You can afford to skim quickly over the applications in the gray boxes and the heavy trig in Ch 5.5. You can omit Ch 5.7. We'll probably skip the MGSP on pg 280. Focus on the HW and the main theorems [the ones in the lectures, such as Thms 5.3.2, 5.6.2 and 5.6.3]. Then read Ch 6.1 (etc) carefully, as usual.

Quiz 6 mainly covers HW 6 and the reading thru 5.5. There may be some TF about the recent lectures (related to Chs. 5.4 and 5.5). Understand what each theorem in these sections says. Know the proofs of Thms 5.1.2, 5.2.1 and 5.3.2, and the discussion of the "normal equations" on pgs 236-237. The TF practice for Quiz 6 [and for Quiz 5] on the exam page may help, too. Review MHW2 for this quiz.

Day	Date	I give you	You give me	Lecture topics	HW
21	T 3/27	Return Q5 + sem-grade		5.4 - I P's (and flex)	3, 7
22	R 3/29			5.5 - ONB	1, 2, 15, 16
23	T 4/3			5.6 - A=QR, proj'ns	1, 2, 5, 7
24	R 4/5	Quiz 6 thru 5.5		6.1- evec.exs, HW	1abcfgk, 2, 3, 4, 5, 6

The final counts 30 points - about half of it will be on topics after Ch 5.5 (like a "Quiz 7") and about half will be review. It cannot be dropped; see the policy page about this, about incompletes, etc. Be sure to do the listed HW problems from Ch.6.3 and 6.4, even though I won't collect them. Omit Ch 5.7 and 6.2.

See the final exam review page. The list of proofs there is correct - 2.2.3, 6.1.1, 6.3.1, 6.3.2 and 6.4.4. Note that all work is due on 4/15 [late HW, regrading requests, excuses, etc]. See also my final lecture topics, an example from my 12/4/06 lecture and the exam page.

I've graded the last of your homework, HW 7 and MHW 3. I've made notes on them, of how many grades I have for you. For example, "6/7" on HW 7 means I am missing one of your 7 HWs and you will get a 0 on it, unless I have made a mistake and you see me about it asap. You are also free to come by to check your other grades. I plan to have normal office hours Thursday, but you'll probably need an appt to see me after that.

Day	Date	I give you	You give me	Lecture topics	HW
25	T 4/10			More 6.1	see above
26	R 4/12			6.3- diag	1, 2, 3, 4, 6, 9
27	T 4/17		MHW3, etc	6.4- A^H, UAU	1, 2, 3, 4, 5
28	R 4/19	Review Day		Ch6 pfs/exs